MBH98: Variance Scaling

I think that Mann et al. are on the horns of an interesting dilemma on variance scaling (and there is no injustice in this.) MàÆàⵢerg et al. [2005], following von Storch et al. [2004], argue that the use of regression-based methods in MBH98/99 result in the lesser variability in the shaft of the hockey-stick. Here are some excerpts:

Different calibration methods (regression in the work of Mann and Jones versus variance scaling in this study) are another reason [for differing variabilities]….Recent findings[von Storch et al., 2004], however, suggest that considerable underestimation of centennial Northern Hemisphere temperature variability may result when regression-based methods, like those used by Mann et al., are applied to noisy proxy data with insufficient spatial representativity…To calibrate the reconstruction, its mean value and variance were adjusted to agree with the instrumental record of Northern Hemisphere annual mean temperatures in the overlapping period AD 1856–1979 (Fig. 2b). This technique avoids the problem with underestimation of low-frequency variability associated with regression-based calibration methods[von Storch et al, 2004]…

The irony of this is that I’m pretty sure that MBH98 contains an unreported variance scaling step. In our emulation of MBH98, we need to carry out a variance scaling after the regression steps in order to get close to their temperature reconstruction so I’m 99% sure that MBH98 has variance scaling as well. (The reason for the hockey stick being the hockey stick is the bristlecone pine imprint as we’ve discussed elsewhere. )

Here’s their dilemma: do they rebut the criticism of von Storch and MàÆàⵢerg by stating that the criticisms are invalid because there is still another undisclosed step in MBH98? But if they do that, then they would have to issue Corrigendum #3 as it were (presuming that a Corrigendum #2 is de facto in place with the incorrectly disclosed PC methods). If they now argued that they included a variance scaling step, would they have to produce their source code (and who knows what lurks there)?

The more important part is that the work of Mann and Jones, nicknamed “Hockey Stick II” has a technique of regression that extends the “stable climate” fantasy back another 1000 years, despite a mountain of other research to the contrary.

“To calibrate the reconstruction, its mean value and variance were adjusted to agree with the instrumental record of Northern Hemisphere annual mean temperatures in the overlapping period AD 1856–1979 (Fig. 2b). ”

This makes no sense to me. Why would one assume that the variance of the reconstruction to be the same as the variance of the instrumental record? It would seem to me that temperature measurements done with a thermometer would have less noise, and therefore a smaller variance due to the noise, than the temperature data derived from the various proxies.

Let me put this another way. You are attempting to measure the amplitude (temperature) of an oscillating system (climate). As a simplified example consider a simple sinusoidal oscillator. We measure the amplitude of this oscillator for some period of time (t1) with an inferior instrument (proxies). We then get a better instrument (thermometers) and continue to measure the oscillator for a period of time (t2). The measurements from time period t1 will have a larger variance, due to the noise, then the measurements from time period t2. If you now adjusted the variance of t1 to agree with t2 you will reduce the amplitude of both the real signal and the noise in t1. IOW you will have attenuated the entire signal in the t1 time period without changing the ratio of noise to the real signal.